9 citations · 29 across the 15 of their papers we have counts for
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Improved bounds for eigenfunctions under random perturbations in negative curvature
Maxime Ingremeau, Martin Vogel
It has been known since the work of Avakumovíc, Hörmander and Levitan that, on any compact smooth Riemannian manifold, if , then $\|ψ_λ\|_{L^\infty} \leq C λ^{\frac…
A trace formula for scattering resonances of unbalanced quantum graphs
Maxime Ingremeau
Given an unbalanced open quantum graph, we derive a formula relating sums over its scattering resonances with integrals outside a strip. We deduce lower bounds on the number of res…
Scattering resonances of large weakly open quantum graphs
Maxime Ingremeau
In this paper, we consider a sequence of open quantum graphs, with uniformly bounded data, and we are interested in the asymptotic distribution of their scattering resonances. Supp…
Empirical spectral measures of quantum graphs in the Benjamini-Schramm limit
Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri +1
We introduce the notion of Benjamini-Schramm convergence for quantum graphs. This notion of convergence, intended to play the role of the already existing notion for discrete graph…
Absolutely Continuous Spectrum for Quantum Trees
Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri +1
We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling…
Quantum ergodicity for large equilateral quantum graphs
Maxime Ingremeau, Mostafa Sabri, Brian Winn
Consider a sequence of finite regular graphs (GN) converging, in the sense of Benjamini-Schramm, to the infinite regular tree. We study the induced quantum graphs with equilateral…
Semiclassical limits of distorted plane waves in chaotic scattering without a pressure condition
Maxime Ingremeau
In this paper, we study the semi-classical behavior of distorted plane waves, on manifolds that are Euclidean near infinity or hyperbolic near infinity, and of non-positive curvatu…
Sharp resolvent bounds and resonance-free regions
Maxime Ingremeau
In this note, we consider semiclassical scattering on a manifold which is Euclidean near infinity or asymptotically hyperbolic. We show that, if the cut-off resolvent satisfies pol…
Equidistribution of Phase Shifts in Obstacle Scattering
Jesse Gell-Redman, Maxime Ingremeau
For scattering off a smooth, strictly convex obstacle with positive curvature, we show that the eigenvalues of the scattering matrix -- the phase shifts --…